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# Mathematics - Algebra - Elasticity and Revenue

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Elasticity and Revenue

Suppose that q = 500 - 2p units of a certain commodity are demanded when p dollars per unit are charged, for
0<=p<=250.

a) Determine where the demand is elastic, inelastic, and of unit elasticity with respect to price.

b) Use the results of part (a) to determine the intervals of increase and decrease of the revenue function and the price at which revenue is maximized.

c) Find the total revenue function explicity and use its first derivative to determine its intervals of increase and decrease and the price at which revenue is maximized.

d) Graph the demand and revenue functions.

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#### Solution Preview

Please see the attachment.

dq/dp = -2. When p E [0, 250], q E [500, 0]

(a) Price elasticity of demand = (dq/dp)(p/q) = -2p/q = -2p/(500 - 2p)
For demand to be elastic, abs[-2p/(500 - 2p)] > 1.

Solving this inequality, we get, 125 < p < 250, that is p E (125, 250) as the price range over which the demand is price-elastic.

For demand to be inelastic, ...

#### Solution Summary

The expert calculates the elasticity and revenues using algebra. A complete, neat and step-by-step solution is provided in the attached file.

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